The volume of the cylinder is approximately 6058.73 cubic meters.
Describe Cylinder?A cylinder is a three-dimensional geometric shape that is similar to a tube. It has two parallel bases that are circular in shape, and its lateral surface is a rectangle. The height of the cylinder is the distance between the two bases. The cylinder has a top base and a bottom base, and these are both circles with the same diameter. The volume of a cylinder can be found by multiplying the area of one of its circular bases by its height. The surface area of a cylinder can be found by adding up the areas of the two circular bases and the lateral surface. Cylinders are widely used in mathematics, engineering, and physics, and they play an important role in the study of various geometric and physical concepts.
Given the diameter of a cylinder is 34m and its height is 27m, we can find the volume of the cylinder using the formula:
Volume = π × (diameter / 2)² × height
Plugging in the values, we get:
Volume = 3.14 × (17 / 2)² × 27
Volume = 3.14 × (8.5)² × 27
Volume = 3.14 × 72.25 × 27
Volume = 6058.73 cubic meters
So, the volume of the cylinder is approximately 6058.73 cubic meters.
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3. A cube has volume 9261 cubic centimetres. Determine the area of one face of the cube.
Show your work. (2 marks)
volume =
3
9261cm
find
surface
area
of this
alde
If the volume of cube is 9261 cubic centimeters, then the surface area of the cube is 2646 square centimeters.
It is given that a cube has volume 9261 cubic centimeters. Let the length of the side of cube is 'a' centimeters.
The formula of volume of a cube is [tex]a^{3}[/tex]
9261 cubic centimeters = [tex]a^{3}[/tex]
a = [tex]\sqrt{9261}[/tex]
a = [tex]\sqrt{21\times21\times21}[/tex]
a = 21 cm
The surface area of cube = [tex]6a^{2}[/tex]
The surface area of cube = [tex]6\times21^{2}[/tex]
The surface area of cube = 2646 square centimeters.
Also the area of one face of the cube = [tex]a^{2}[/tex]
The area of one face of the cube is 441 square centimeters.
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Select the values that are solutions to the inequality x2 + 3x – 4 > 0. –6 –2 0 5
The values that are solutions to inequality are -6 and 5.
Options A and D are the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
x² + 3x - 4 > 0
Now,
Substituting x = -6, -2, 0, 5
(-6)² + 3(-6) - 4 > 0
36 - 18 - 4 > 0
36 - 22 > 0
14 > 0
True.
x² + 3x - 4 > 0
(-2)² + 3 x (-2) - 4 > 0
4 - 6 - 4 > 0
-6 > 0
This is not true.
x² + 3x - 4 > 0
0 + 3 x 0 - 4 > 0
0 + 0 - 4 > 0
-4 > 0
This is not true.
x² + 3x - 4 > 0
5² + 3 x 5 - 4 > 0
25 + 15 - 4 > 0
40 - 4 > 0
36 > 0
This is true.
Thus,
-6 and 5 are the solutions to inequality.
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(i) Are there values of k such that the curve y = (k + 3)x² - 3x lies completely above the line y = x + k? Justify your answer. (ii) Explain the relationship between the curve and the line in part (i).
Answer:
(i) No
(ii) The line and curve always intersect in two places
Step-by-step explanation:
You want to know if there are values of k such that the curve y = (k+3)x²-3x lies completely above the line y = x+k. And you want to know the relationship between the line and the curve.
(i) DiscriminantThe number of points of intersection between the line and the curve can be found by considering the discriminant of the quadratic equation for the difference of the y-values.
The line and curve will intersect when their y-values are equal:
(k +3)x² -3x = x +k
(k +3)x² -4x -k = 0 . . . . . compare to ax²+bx+c=0
The discriminant is the value of b²-4ac, so is ...
d = (-4)² -4(k+3)(-k) = 16 +4k(k -3)
Writing this in vertex form, we have ...
4(k² -3k) +16 = d
4(k² -3k +2.25) +16 -4(2.25) = d . . . . . "complete the square"
4(k -1.5)² +7 = d
The square is always positive, and it is added to a positive value (7), so the discriminant d is always positive. This means there are always two points of intersection between the curve and the line.
(ii) RelationshipAs we saw above, the line and curve will always intersect at two points. This means there are always parts of the curve both above and below the line.
__
Additional comment
For the value k=-3, the "curve" becomes a line with slope -3 through the origin. It will intersect the line y=x-3 at one point. It seems reasonable to exclude that case from consideration.
A string with a linear density of 2 kg/m and a tension of 100 N is fixed at both ends. Determine the frequency of the first harmonic of the string.
Step-by-step explanation:
The frequency of the first harmonic of a string fixed at both ends can be determined using the formula:
f = (1 / 2L) * √(T / μ)
where f is the frequency, L is the length of the string, T is the tension, and μ is the linear mass density. Plugging in the given values:
f = (1 / 2 * L) * √(100 N / 2 kg/m)
= (1 / 2 * L) * √(50 N/m)
So, the frequency of the first harmonic depends on the length of the string, which is not specified in the problem.
Answer:
Step-by-step explanation:
The frequency of the first harmonic of a string fixed at both ends can be calculated using the formula:
f = (1 / 2L) * (T / μ)^(1/2)
where:
f = frequency
L = length of the string
T = tension
μ = linear density of the string
Plugging in the values:
f = (1 / 2 * L) * (100 N / 2 kg/m)^(1/2)
f = (1 / 2L) * (10 N/kg)^(1/2)
We don't have the length of the string, L, so we can't calculate the frequency.
if you were to construct a pareto chart (using the rule suggested in the book), how would the second bar in the graph be labeled?
When constructing a Pareto chart, the second bar would be labeled with the name of the item that has the second highest frequency or impact, as determined by the data being analyzed.
In a Pareto chart, the bars are typically labeled with the names of the items being analyzed, and the height of each bar represents the frequency or the impact of each item. The bars are typically ordered from largest to smallest, with the largest bar appearing on the left and the smallest bar on the right.
It is worth noting that the "rule" you referred to in the book might refer to the 80-20 rule, also known as the Pareto principle. This rule states that roughly 80% of the effects come from 20% of the causes. In the context of a Pareto chart, this means that you might expect the first few bars to represent a large portion of the total frequency or impact, while the later bars represent a much smaller portion.
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Tyrice put 4 cookies in each of 7 bags.how many cookies in all did he put in the bags.
Answer:
Step-by-step explanation:
4 cookies times 7 bags
4x7=28
Abdoulaye spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 5925 feet. Abdoulaye initially measures an angle of elevation of 16
∘
∘
to the plane at point
�
A. At some later time, he measures an angle of elevation of 31
∘
∘
to the plane at point
�
B. Find the distance the plane traveled from point
�
A to point
�
B. Round your answer to the nearest tenth of a foot if necessary.
The distance the plane traveled from point A to point B is 10,802.1 feet.
What are trigonometric functions?Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Given the height of the plane = 5925 feet
let the distance between A to B be x and distance from B to the position of the plane is y as shown in the image,
angle of elevation from point A = 16°
the angle of elevation from point B = 31°
using trigonometric functions,
tanα = perpendicular/base
base = x + y
perpendicular = 5925 feet
tan(16) = 5925/(x + y)
x + y = 5925/tan(16)
y = 5925/tan(16) - x.........(1)
and tan(32) = 5925/y
y = 5925/tan(32)
substitute the value of y from equation 1
5925/tan(16) - x = 5925/tan(32)
5925/tan(16) - 5925/tan(32) = x
x = 10,802.1 feet
Hence the distance covered by points A to B is 10,802.1 feet.
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Fill in the blanks below..
(a) A car corporation produced 1980 more cars this month than last.
Write a signed number to represent this month's change in production.
(b) The temperature fell by 18 degrees Fahrenheit today.
Write a signed number to represent this temperature change
What is the longest line segment that can be drawn in a right rectangular prism that is 14 cm long, 13 cm wide, and 9 cm tall?
The longest line segment that can be drawn in a right rectangular prism is 21.1 cm.
Let us assume the right rectangular prism be labelled as shown in figure. Now the longest possible line here is the diagonal between two most far points like A and G. So, finding the length of AG from triangle AGC.
But, prior to this calculation, we need to find AC. It will be calculated from the traingle ABC.
So, AC² = AB² + BC²
AC² = 14² + 13²
AC² = 196 + 169
AC² = 365
AC = 19.1 cm
Now, finding length of AG.
AG² = AC² + GC²
AG² = 365 + 9²
AG² = 365 + 81
AG² = 446 cm
AG = ✓446
AG = 21.1 cm
Thus, the diagonal AG is 21.1 cm.
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The function f is defined by f (x) = 50.3%. The function g is defined by g(x) = a. b
Here are graphs of f and g.
g
X
1. How does a compare to 50? Explain how you know.
2. How does b compare to 3? Explain how you know.
On solving the provided question, we can say that Point (1,1) must be on the graph of f if point (x,1) is on the graph of f. (x).
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
Given that y=f(x) and g(x)=f (x)
Flipping the graph of y=f(x) across the y axis, as shown in the image, will give you the graph of g(x)=f(x).
For instance, the point (2,2) must be on the graph of f if point (2,2) is on the graph of f(x) (x).
Point (3,1) must be on the graph of f if point (3,1) is on the graph of f(x) (x).
Point (1,1) must be on the graph of f if point (1,1) is on the graph of f(x) (x).
Point (1,1) must be on the graph of f if point (x,1) is on the graph of f. (x).
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Solve for z zz. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. − 4 z + 31 ≥ 17 z + 23 −4z+31≥17z+23
[tex]-4z+31\geqslant 17z+23\implies 31\geqslant 13z+23\implies 8\geqslant 13z\implies \cfrac{8}{13}\geqslant z[/tex]
list the elements of the Sets (1) (AnB)' UC (ii) (AUC) 'n B (iii) (AUBUC)'
Answer:
(i) The complement of the intersection of Sets A and B, denoted by (A∩B)', is the set of all elements that are not in the intersection of Sets A and B. It can be found by taking the union of the complements of Sets A and B, denoted by A' and B'. Hence, (AnB)' = A' U B'.
(ii) The complement of the union of Sets A and C, denoted by (A U C)', is the set of all elements that are not in the union of Sets A and C. It can be found by taking the intersection of the complements of Sets A and C. Hence, (A U C)' = A' ∩ C'.
(iii) The complement of the union of Sets A, B, and C, denoted by (A U B U C)', is the set of all elements that are not in the union of Sets A, B, and C. It can be found by taking the intersection of the complements of Sets A, B, and C. Hence, (A U B U C)' = A' ∩ B' ∩ C'.
Two apple trees are going next to each other the oldest tree has a 36 ft Shadow the smaller Creek has a 12-in shadow and there is 8 ft tall how tall is the older tree
The old tree in 54 feet height.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that Two apple trees are going next to each other
the oldest tree has a 36 ft Shadow
the smaller Creek has a 12-in shadow and the tree is 8 ft tall.
We need to find the height of the older tree.
Let x be the height of older tree.
36/x=8/12
36×12=8x
432=8x
Divide both sides by 8
54=x
Hence, the old tree in 54 feet height.
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Jared budges 860 each month for this expenses what percent of his net monthly income is that if his annual net income is 24,348
a man has two shirts and nine ties asuuming that they all match how many diferent shirtt and tie combination can he wear
The man can wear 27 different shirt and tie combinations.
Therefore the answer is 27.
The number of different shirt and tie combinations that a man can wear can be calculated by multiplying the number of choices for each item.
Number of choices for shirts = 3
Number of choices for ties = 9
Since the man has three different shirts and nine different ties, and each shirt can be paired with any one of the nine ties, the number of combinations is:
Combinations = 3 * 9 = 27
So the man can wear 27 different shirt and tie combinations.
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Describe the transformations that maps figure RSTU onto figure R1 S1 T1 U1
Problems had to do with translation and units
Figure RSTU is transformed into Figure R1 S T 1 U1 by moving down two units and reflecting on the y axis.
what is transformation ?Deformations are four alternative approaches that can be utilized to change a point, line, or mathematical figure's orientation and/or shape. Both the Pre-Image, who describes the shape of the object there at initial state, and the Photograph, which describes the final state and location of the object following change, are words. Translations, reflection, and dilations are the three types of transformations that can be differentiated. A function can undergo two different types mathematical transformations: vertical (it affects the y-values) and sideways (affects the x-values). Its function's equation is provided below, and it comprises the share the information variables (a, b, h, and k). modifying the log. observation. even by square root, invert.
given
From the figure RSTU to R'S'T'U' R moved from P(5,2) to P(-3,0), translating 8 units to the left.
Hence, 5-(-3)= 8 = 2-0 = 0.
Down two units.
as well as reflection on the y axis.
Figure RSTU is transformed into Figure R1 S T 1 U1 by moving down two units and reflecting on the y axis.
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The population of India was 1,324,671,354 in 2016. Round the population to the nearest million people.
Answer:
1,325,000,000 people
Step-by-step explanation:
Million = 1,000,000
Number = 1,324,671,354
The 1st 4 is in the millionth place. 6 > 4 so round 4 up to 5.
Rounded = 1,325,000,000 people
in the given figure AB || CD PROVE THAT p+q+r = 180
The sum of angles p, q, and r is equal to 180 degrees.
A degree is a unit of measurement used in geometry to represent angles.
To prove this, we will use the concept of alternate interior angles. Alternate interior angles are angles that are formed on the inside of the two lines when they are parallel to each other. Since AB || CD, alternate interior angles p and q are equal.
We know that the sum of angles in a triangle is equal to 180 degrees. In this case, we have a triangle ABC with angles p, q, and r. Hence,
=> p + q + r = 180 degrees.
Next, since p and q are equal, we can represent them as p = q. Now, substituting the value of q into the above equation, we get:
=> p + p + r = 180 degrees.
This can be simplified to 2p + r = 180 degrees. But since p = q, we can replace p with q. Hence,
=> 2q + r = 180 degrees.
Finally, substituting the value of p = q into the above equation, we get:
=> 2p + r = 180 degrees.
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Mrs. Klein went to Target in search of a good deal on laundry detergent (Owen is one messy boy!). She found Tide was $15.99 with 20% off. Gain was $17.55 with 25% off. She has a target red card and gets 5% off her total purchase.
The product which cost less is Tide which has a cost value of $15.99 with 20% off.
What is Cost?This is referred to as the expenditure required to create and sell products and services, or to acquire assets.
Tide was $15.99 with 20% off which when calculated = 20/100 × $15.99 = $3.198.
Gain was $17.55 with 25% off which when calculated = 25/100 × $17.55 = $4.388.
Therefore the cheaper alternative will be Tide detergent.
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The full question:
Mrs. Klein went to Target in search of a good deal on laundry detergent (Owen is one messy boy!). She found Tide was $15.99 with 20% off. Gain was $17.55 with 25% off. She has a target red card and gets 5% off her total purchase. which one of the products costs less?
The notation "f(x)" (f of x) is another way of representing y-values in a function
True
False
need help is it true or false
8. Express the area of the figure as a monomial.
p2q4 and p2q4
The area of the figure as a monomial with the sides [tex]p^{2} q^{4}[/tex] and [tex]p^{2} q^{4}[/tex] is [tex]p^{4} q^{8}[/tex].
As per the given data we to express the area of the figure as a monomial.
Figure attached at the end of solution.
What is monomial?A polynomial with only one term is called a monomial. An algebraic expression known as a monomial has only one term but might have more than one variable and a higher degree.
As the sides are equal we use the area of the square formula.
Area of the square formula:
The formula for the area of a square is side × side
Simple multiplication is the answer to the equation.
Area of the given figure:
= [tex]p^{2} q^{4} \times p^{2} q^{4}[/tex]
= [tex]p^{4} q^{8}[/tex]
[tex]p^{4} q^{8}[/tex] is a monomial as it is expressed as a single term.
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a rectangular table top is three times as it is wide. it's width is 2 meters. what is the area of the table top
12m² is the area of the table top in rectangle .
What is a rectangle, exactly?
The parallel sides of a rectangle are equal to one another, and each of its four vertices is 90 degrees, making it a form of quadrilateral. As a result, it is sometimes referred to as an equiangular quadrilateral.
The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.
area = length x width
We know that the width is 2 meters, and since the length is three times the width, the length would be 6 meters.
Therefore, the area of the table = 2 x 6 = 12 m2.
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when determining the approximate width of the bins for a frequency distribution of quantitative data, the difference of what two values is divided by the number of bins?
The difference of the maximum and minimum values is divided by the number of bins.
1. Identify the maximum and minimum values of the quantitative data
2. Subtract the minimum value from the maximum value to get the difference
3. Divide the difference by the number of bins to get the approximate width of each bin
The width of the bins in a frequency distribution of quantitative data can be estimated by dividing the difference between the maximum and minimum values of the data by the desired number of bins. This will provide an approximate size for each bin, which can then be used to construct the frequency distribution.
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Find the area of the circle shown.
Use 3.14 as an approximation of pi.Round your answer to the nearest tenth
Answer: A = 19.6^2 ( 19.6 to the 2nd power )
Step-by-step explanation:
Area of a circle = 3.14 * r^2
A = 3.14 * 2.5^2
A = 19.625
19.625 rounded to the nearest tenth is 19.6
According to the information we can infer that the area of the circle with a radius of 2.5 is approximately 19.63 square units.
How to calculate the area of the circle?The area of a circle is given by the formula A = πr², where A represents the area and r represents the radius.
In this case, the radius is given as 2.5 units. Substituting this value into the formula, we have:
A = π(2.5)²A = π(6.25)Using an approximate value of π as 3.14159, we can calculate the area:
A ≈ 3.14159 × 6.25A ≈ 19.63So we can conclude that the area of the circle with a radius of 2.5 units is approximately 19.63 square units.
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Draw a dilation of the figure around the origin using the given scale factor.
k=1/4
After dilation with the scale factor 1/4 is A'(0, 1), B'(1, 1) and C'(-1, -1).
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given that, the scale factor is k= 1/4.
From the given figure, vertices of triangle ABC are
A(0, 4), B(4, 4) and C(-4, -4)
After dilation with the scale factor 1/4, we get
A(0, 4)→1/4 (0, 4) =A'(0, 1)
B(4, 4)→1/4 (4, 4) =B'(1, 1)
C(-4, -4)→1/4 (-4, -4) =C'(-1, -1)
Therefore, after dilation with the scale factor 1/4 is A'(0, 1), B'(1, 1) and C'(-1, -1).
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what is 28 divided by the square root of 2
Answer:
14√2
Step-by-step explanation:
28/√2
Since you can't have a square root as the denominator of a fraction, we must multiply the denominator and the numerator to get rid of the square root.
Hence,
28 x √2 , √2 x √2
Your problem would now be:
28√2 / 2
Reduce the fraction by canceling out the common factor of 2
ANS = 14√2
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Six ounces of orange juice contain 75 calories. About how many calories are in fourteen ounces of orange juice ? Part A. Write a proportion, make sure to include units. Let x= the unknown calories. Part B. Solve for X
Answer:
175 calories
Step-by-step explanation:
75 / 6 = 12.5
12.5 x 14 = 175
x = 12.5 x 14
What is the measure of angle R?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
m∠R =
The measure of the angles of the triangles are 90° , 67.380° and 22.620°
What is the law of sines?The relationship between a triangle's sides and angles is provided by the Law of Sines. Trigonometry's law of sines can be expressed as a/sinA = b/sinB = c/sinC, where a, b, and c are the lengths of the triangle's sides, and A, B, and C are the triangle's respective opposite angles.
Law of Sines :
a / sin A = b / sin B = c / sin C
Given data ,
Let the triangle be represented as ΔPQR
Now , the measure of ∠PQR = 90°
The measure of side PR = 13 cm
The measure of side PQ = 5 cm
The measure of side QR = 12 cm
From the law of sines , we get
a / sin A = b / sin B = c / sin C
Substituting the value sin the equation , we get
12 / sin P = 13 / sin 90°
From the trigonometric relations , sin 90° = 1
So , Multiply by sin P on both sides of the equation , we get
sin P = 12/13
Taking inverse on both sides of the equation , we get
sin⁻¹ ( 12/13 ) = 67.380°
Therefore , the measure of ∠QPR = 67.380°
And , the measure of ∠PRQ = 180 - ( 90° + 67.380° )
The measure of ∠PRQ = 22.620°
Hence , the angles of triangles is solved
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A car sales person makes $7.00 per hour plus $100.00 for every car sold. Which expression represents the amount in dollars the salesperson makes, before taxes, if x cars are sold in 40 hours?
The expression that represents the amount in dollars the salesperson makes, before taxes, would be equal to 7x + 100 = 40.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol that can also be used to indicate the logical syntax's order of operations and other features.
Given that car sales person makes $7.00 per hour plus $100.00 for every car sold.
Therefore, we have,
7x + 100 = 40
The expression that represents the amount in dollars the salesperson makes, 7x + 100 = 40.
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help please i’m tired and i just want to finish this and go to bed
Answer: 112i + 85.8j
Step-by-step explanation:
Answer:
[tex]\vec{H}=-32.1\:\hat{i}+79.6\:\hat{j}[/tex]
Step-by-step explanation:
VectorsThe magnitude of a vector gives the length of the line segment.The direction of a vector gives the angle the line forms with the positive x-axis.To find the components of a vector given its magnitude and direction, use the following formula:
[tex]\large\boxed{\vec{u}=\left(||\vec{u}|| \cos(\theta),|| \vec{u}|| \sin(\theta)\right)}[/tex]
where:
[tex]||\vec{u}||[/tex] is the magnitudeθ is the angle (in degrees)Given:
[tex]||\vec{H}||=85.8[/tex][tex]\theta=112^{\circ}[/tex]Substitute the given values into the formula:
[tex]\vec{H}=\left(85.8 \cos(112^{\circ}),85.8 \sin(112^{\circ})\right)[/tex]
[tex]\vec{H}=\left(-32.1, 79.6\right)[/tex]
Therefore:
[tex]\vec{H}=-32.1\:\hat{i}+79.6\:\hat{j}[/tex]